acid, acetic ether, monochlor-acetic ether, benzene, dimethyl-aniline, wood-spirit, and alcohol. The observations were all made with the Wild's polariscope. In all the solutions the specific rotation experienced a decrease with the increase of inactive substance q, but at a rate varying widely, and depending on the nature of the latter. As the diagram, Fig. 19, shows, the rate of decrease in each case is expressed pretty closely by a straight line when acetic acid, acetic ether, monochlor-acetic ether, benzene, or dimethyl-aniline is used as solvent, and hence for these substances the formula [a] = A + Bq may be used. With wood-spirit and alcohol, on the contrary, the deviations from a straight line are too considerable, and in these cases the [a]D=54.38-0·1614q +0.0003690 q2 (1 IV. 43.33 -0.33 formula [a] = A + Bq + Cq2 must be taken as the basis of calculation. The table annexed shows (1) the values of constants A and B, calculated from the several solutions; (2) the derived interpolationformulæ obtained by putting in the mean values; (3) the specific rotation of the solutions employed calculated from these equations, and the differences between these and the observed values, as given in the preceding table (p. 85). Comparing now with each other the values for constant A derived from different solvents, we find an agreement which, in view of the large amount of extrapolation from q = 0 onwards, varying from 35 to 50 per cent., must be regarded as very close, and the mean of their values may accordingly be taken as the true specific rotation of pure camphor. The values for constant B, on the contrary, exhibit very marked variations. Calculating the specific rotation from the same formulæ, by putting in limiting values q = 0 and q = 100, we obtain the following as the range of variation which the rotatory power of camphor may undergo under the influence of various inactive liquids employed as solvents. Lastly, taking the mean of the values obtained for the pure substance, we have as the true specific rotation AD of camphor, at a temperature of 20° Cent., 2 § 37. In the same way the true rotation-constant of cane-sugar was determined by Tollens,1 and simultaneously by Schmitz, water being the only solvent used. In the case of sugar, the specific rotation 2 Schmitz: Idem., 1877, 1414; also, Zeitsch. d. Ver. für Rübenzuckerind. 1878, 48. increases with dilution, or, conversely, decreases with increase of concentration, but the variations are small. Tollens examined seventeen solutions, of which the most concentrated, with 69-2144 per cent. by weight of sugar, gave a specific rotation [a] = 65-490°, and the most dilute with 3.8202 per cent., gave [a]û = 66·803°. From the experimental results were derived the following interpolation-formulæ for the calculation of the specific rotation of any given solution, by putting in values for p, percentage of sugar, and q, percentage of water respectively : : (a) For strong Solutions, containing from 18 to 69 per cent. of Sugar. 66.3860·015035 p -0.0003986 p2. I. II. [a]D = [a] = 63·904 + 0.064686 g 0.0003986 q2. q (b) For weak Solutions containing less than 18 per cent. D 0.000052462 p2. [a]D = 64-730+ 0.026045 q- 0·000052462 q2. III. IV. The equation with reference to q, derived from these observations, stands [a]D = 64.156+0.051596 q- 0.00028052 q2; according to which, the rotation-constant for pure sugar at a temperature of 20° Cent. is AD = 64.16°, |